Core Theorems in The Generalized Statistical Sense

Yıl 2018, Cilt: 8, 16 - 21, 30.06.2018

Emre Taş Tugba Yurdakadim

Öz

The main purpose of the paper is to give some results concerning with the generalized statistical core of a bounded sequence via $\mathfrak{B}$-statistical convergence where $\mathfrak{B}=(B_{i})$ is a sequence of infinite matrices. We characterize the matrix class $(st_{\mathfrak{B}}\cap X,Y)$ for certain sequence spaces $X$ and $Y$. Here $st_{\mathfrak{B}}$ is the set of all $\mathfrak{B}$-statistically convergent sequences. Finally we answer the multipliers and factorization problem for $\mathfrak{B}$-statistically convergent sequences.

Anahtar Kelimeler

Knopp core, generalized statistical convergence, $\mathfrak{B}$- statistical limit superior and inferior

Kaynakça

• Bell, H. T., Order summability and almost convergence. Proc. Amer. Math. Soc. 38 (1973), 548-552.
• Connor, J., Demirci, K., Orhan, C., Multipliers and factorization for bounded statistically convergence sequences. Analysis (Munich) 22 (2002), 321-333.
• Demirci, K., $A$-statistical core of a sequence. Demonstratio Math. 33 (2000), 343-353.
• Demirci, K., I-limit superior and limit inferior. Math. Commun. 6 (2001), 165-172.
• Dirik, F., Demirci, K., B-statistical approximation for periodic functions. Studia Sci. Math. Hungar., 47 (2009), 321-332.
• Dirik, F., Demirci, K., Korovkin type approximation theorems in B-statistical sense. Math. Comput. Modelling 49 (2009), 2037-2044.
• Fridy, J. A., Orhan, C., Statistical limit superior and limit inferior. Proc. Amer. Math. Soc. 125 (1997), 3625-3631.
• Khan, M. K., Orhan, C., Matrix characterization of A-statistical convergence. J. Math. Anal. Appl. 335 (2007), 406-417.
• Kolk, E., Matrix summability of statistically convergent sequences. Analysis 13 (1993), 77-83.
• Kolk, E., Inclusion relations between the statistical convergence and strong summability. Acta et Comm. Univ. Tartu. Math. 2 (1998), 39-54.
• Maddox, I. J., Some analogues of Knopp's core theorem. Internat. J. Math. and Math. Sci. 2 (1979), 605-614.
• Mursaleen, M., Edely, O. H. H., Generalized statistical convergence. Information Sciences 162 (2004), 287-294.
• Orhan, C., Sublinear functionals and Knopp's core theorem. Internat. J. Math. and Math. Sci. 13 (1990), 461-468.
• Orhan, S., Dirik, F., Strong and A-statistical comparisons for double sequences and multipliers, Studia Universitatis Babes¸-Bolyai Mathematica, 58(2013), 213–223.
• Özgüç, I. S., Yurdakadim, T., On quasi statistical convergence. Commun. Fac. Sci. Univ. Ank. Series A1 61 (2012), 11-17.
• Shcherbakov, A. A., Kernels of sequences of complex numbers and their regular transformations. Math. Notes 22 (1977), 948-953.